Question

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An inspector visited a forestry clearcut area that had been replanted with seedlings a year earlier. Out of 50 seedlings inspected, 14 had survived.
a) Calculate confidence intervals for p = the overall 1-year survival rate for all replanted seedlings in this clearcut area, for:
i. LOC = 90%
ii. LOC = 95%
b) Comment on whether or not the 90% CI would support a claim that the actual overall survival rate for all replanted seedlings in this clearcut area is 40%.
c) Would your answer for Part (b) remain the same or change for LOC = 95%? Explain your answer.
d) Estimate the minimum sample size required to generate an estimate of p to within ±2.5% at LOC = 95%, assuming that there is no previous sample data to use.

Answer 1

(a)

(i)

n = 50

= 14/50 = 0.28

= 0.10

From Table, critical values of Z = 1.645

90% Confidence Interval:

So,

Answer is:

(0.176, 0.384)

(i)

n = 50

= 14/50 = 0.28

= 0.05

From Table, critical values of Z = 1.96

95% Confidence Interval:

So,

Answer is:

(0.156, 0.404)

(b)

Since the value of p = 0.40 is not included in the 90% Confidence Interval (0.176, 0.384), we conclude that the 90% CI would not support a claim that the actual overall survival rate for all replanted seedlings in this clearcut area is 40%.

(c)

Since the value of p = 0.40 is included in the 95% Confidence Interval (0.156, 0.404) , we conclude that the 95% CI would support a claim that the actual overall survival rate for all replanted seedlings in this clearcut area is 40%.

(d)

Minimum Sample Size (n)is given by:

So,

Answer is:

1240